REBayes: Tncpmix – R documentation

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Tncpmix

NPMLE for Student t non-centrality parameter mixtures

Description

Kiefer Wolfowitz NPMLE for Student t non-centrality parameter mixtures Model: y_{ig} = mu_{g} + e_{ig}, e_{ig} ~ N(0,sigma_{g}^{2}) x is the vector of t statistics for all groups, which follows t dist if mu_g = 0, and noncentral t dist if mu_g \neq 0, with ncp_{g} = μ_g / σ_{g}. This leads to a mixture of t distribution with ncp as the mixing parameter. df (degree of freedom) is determined by the group size in the simplest case.

Usage

Tncpmix(x, v = 300, u = 300, df = 1, hist = FALSE,
  weights = NULL, ...)

Arguments

`x`	Data: Sample Observations
`v`	bin boundaries defaults to equal spacing of length v
`u`	bin boundaries for histogram binning: defaults to equal spacing
`df`	Number of degrees of freedom of Student base density
`hist`	If TRUE then aggregate x to histogram weights
`weights`	replicate weights for x obervations, should sum to 1
`...`	optional parameters passed to KWDual to control optimization

Value

An object of class density with components:

`x`	midpoints of evaluation on the domain of the mixing density
`y`	estimated function values at the points x of the mixing density
`g`	estimated function values at the observed points of mixture density
`logLik`	Log likelihood value at the proposed solution
`dy`	Bayes rule estimates of location at x
`status`	Mosek exit code

Author(s)

Roger Koenker

References

Kiefer, J. and J. Wolfowitz Consistency of the Maximum Likelihood Estimator in the Presence of Infinitely Many Incidental Parameters Ann. Math. Statist. 27, (1956), 887-906.

Koenker, R. and J. Gu, (2017) REBayes: An R Package for Empirical Bayes Mixture Methods, Journal of Statistical Software, 82, 1–26.